RS Aggarwal solutions for Mathematics [English] Class 10 chapter 14 - Height and Distance [Latest edition]

A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot of the tower, the angle of elevation of its top is found to be 60°. Find the height of the tower. [Take `sqrt(3)` =1.732 ]

A kite is flying at a height of 75 in from the level ground, attached to a string inclined at 60°. to the horizontal. Find the length of the string, assuming that there is no slack in it.
[Take `sqrt(3)` =1.732 ]

An observer 1.5m tall is 30 away from a chimney. The angle of elevation of the top of the chimney from his eye is 60 . Find the height of the chimney.

The angles of elevation of the top of a tower from two points at distance of 5 metres and 20 metres from the base of the tower and is the same straight line with it, are complementary. Find the height of the tower.

The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45 . If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60 , then find the height of the flagstaff [Use `sqrt(3)` 1.732]

From a point on the ground 40m away from the foot of a tower, the angle of elevation of the top of the tower is 30 . The angle of elevation of the top of a water tank (on the top of the tower) is 45 , Find (i) the height of the tower, (ii) the depth of the tank.

The vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is
30 and that of the top of the flagstaff 60 . Find the height of the tower
[Use `sqrt(3)` 1.732 ]

A statue 1.46m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the status is 60 and from the same point, the angle of elevation of the top of the pedestal is 45 . Find the height of the pedestal.

The angle of elevation of the top of an unfinished tower at a distance of 75m from its base is 30° .How much higher must the tower be raised so that the angle of elevation of its top at the same point may be 60 . 

On a horizonal plane there is a vertical tower with a flagpole on the top of the tower. At a point, 9 meters away from the foot of the tower, the angle of elevation of the top and bottom of the flagpole are 60 and 30 respectively. Find the height of the tower and the flagpole mounted on it.

Two poles of equal heights are standing opposite to each other on either side of the road which is 80m wide, From a point P between them on the road, the angle of elevation of the top of one pole is 60 and the angle of depression from the top of another pole at P is 30 . Find the height of each pole and distance of the point P from the poles.

Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30 and 45 respectively. If the height of the tower is 50 meters, find the distance between the two men.

From the point of a tower 100m high, a man observe two cars on the opposite sides to the tower with angles of depression 30° and 45 respectively. Find the distance between the cars

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car as an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.

The angle of elevation on the top of a building from the foot of a tower is 30° . The angle of elevation of the top of the tower when seen from the top of the second water is 60° .If the tower is 60m high, find the height of the building.

The horizontal distance between two towers is 60 meters. The angle of depression of the top of the first tower when seen from the top of the second tower is 30° . If the height of the second tower is 90 meters. Find the height of the first tower.

The angle of elevation of the top of a chimney form the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30° . If the height of the tower is 40 meters. Find the height of the chimney.

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

The angle of depression form the top of a tower of a point A on the ground is 30° . On moving a distance of 20 meters from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower to from the point B is 60° . Find the height of the tower and its distance from the point A.

The angle of elevation of the top of a vertical tower from a point on the ground is 60° . From another point 10 m vertically above the first, its angle of elevation is 30° .Find the height of the tower.

The angles of depression of the top and bottom of a tower as seen from the top of a 60  `sqrt(3)` m high cliff are 45° and 60° respectively. Find the height of the tower.

A man on the deck of a ship, 16m above water level, observe that that angle of elevation and depression respectively of the top and bottom of a cliff are 60° and 30° . Calculate the distance of the cliff from the ship and height of the cliff.

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60° . At a point Y, 40m vertically above X, the angle of elevation is 45° . Find the height of tower PQ.

The angle of elevation of an aeroplane from a point on the ground is 45° after flying for 15seconds, the elevation changes to 30° . If the aeroplane is flying at a height of 2500 meters, find the speed of the areoplane.

The angle of elevation of the top of a tower from ta point on the same level as the foot of the tower is 30° . On advancing 150 m towards foot of the tower, the angle of elevation becomes 60° Show that the height of the tower is 129.9 metres.

As observed form the top of a lighthouse, 100m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° and 60° . Determine the distance travelled by the ship during the period of observation.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 2.5m from the banks, find the width of the river.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m. from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

A ladder of length 6meters makes an angle of 45° with the floor while leaning against one wall of a room. If the fort of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60° with the floor. Find the
distance between two walls of the room.

From the top of a vertical tower, the angles depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45°  and 60° . If the cars are 100 m apart and are on the same side of the tower, find the height of the tower.

An electrician has to repair an electric fault on a pole of height 4 meters. He needs to reach a point 1 meter below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of 60° to the horizontal would enable him to reach the required position?

From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30° and 60° respectively. Find

1) the horizontal distance between AB and CD

2) the height of the lamp post.

3) the difference between the heights of the building and the lamp post.